Dependence of Variational Perturbation Expansions on Strong-Coupling Behavior. Inapplicability of delta-Expansion to Field Theory

TL;DR

This paper demonstrates that neglecting the Wegner exponent omega in variational quantum field theory leads to divergence or incorrect limits, invalidating the delta-expansion method for such applications.

Contribution

It highlights the critical importance of the Wegner exponent omega in variational approaches to quantum field theory and exposes the limitations of the delta-expansion method.

Findings

Neglecting omega causes divergence in variational methods.

Proper accounting of omega ensures convergence to correct limits.

The delta-expansion is invalid for quantum field theory without considering omega.

Abstract

We show that in applications of variational theory to quantum field theory it is essential to account for the correct Wegner exponent omega governing the approach to the strong-coupling, or scaling limit. Otherwise the procedure either does not converge at all or to the wrong limit. This invalidates all papers applying the so-called delta-expansion to quantum field theory.